Doppler-operated computers which perform plane D.R. navigation are currently offered to the airlines. A datum track and distance to go are set; from the time of selecting ON, the computer resolves small elements of distance run (input doppler and heading reference) as follows:

Change in across-track dist. = element of dist. run × sin (actual tr. − set tr.)

Change in along-track dist. = element of dist. run × cos (actual tr. − set tr.)

These relations are true for a plane Earth.